In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint introduces a nonlocal Lagrange multiplier in the penalized equation, giving rise to a nonlocal parabolic problem. We introduce a compatibility condition relating the initial datum and the obstacle function which ensures global in time existence of solution. This is not a smoothness condition, but relates to the propagation of the support of the initial datum.
Mots clés : Hyperbolic conservation law, Obstacle problem, Mass conservation, Nonlocal parabolic equation, Free boundary problem
@article{AIHPC_2017__34_1_221_0, author = {Amorim, Paulo and Neves, Wladimir and Rodrigues, Jos\'e Francisco}, title = {The obstacle-mass constraint problem for hyperbolic conservation laws. {Solvability}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {221--248}, publisher = {Elsevier}, volume = {34}, number = {1}, year = {2017}, doi = {10.1016/j.anihpc.2015.11.003}, mrnumber = {3592685}, zbl = {1357.35215}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2015.11.003/} }
TY - JOUR AU - Amorim, Paulo AU - Neves, Wladimir AU - Rodrigues, José Francisco TI - The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 221 EP - 248 VL - 34 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2015.11.003/ DO - 10.1016/j.anihpc.2015.11.003 LA - en ID - AIHPC_2017__34_1_221_0 ER -
%0 Journal Article %A Amorim, Paulo %A Neves, Wladimir %A Rodrigues, José Francisco %T The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 221-248 %V 34 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2015.11.003/ %R 10.1016/j.anihpc.2015.11.003 %G en %F AIHPC_2017__34_1_221_0
Amorim, Paulo; Neves, Wladimir; Rodrigues, José Francisco. The obstacle-mass constraint problem for hyperbolic conservation laws. Solvability. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 1, pp. 221-248. doi : 10.1016/j.anihpc.2015.11.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2015.11.003/
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